Given $ m \angle MON = 3x - 11$, and $ m \angle LOM = 3x + 125$, find $m\angle LOM$. $O$ $L$ $N$ $M$
Explanation: From the diagram, we see that together ${\angle LOM}$ and ${\angle MON}$ form ${\angle LON}$ , so $ {m\angle LOM} + {m\angle MON} = {m\angle LON}$ Since $\angle LON$ is a straight angle, we know ${m\angle LON = 180}$ Substitute in the expressions that were given for each measure: $ {3x + 125} + {3x - 11} = {180}$ Combine like terms: $ 6x + 114 = 180$ Subtract $114$ from both sides: $ 6x = 66$ Divide both sides by $6$ to find $x$ $ x = 11$ Substitute $11$ for $x$ in the expression that was given for $m\angle LOM$ $ m\angle LOM = 3({11}) + 125$ Simplify: $ {m\angle LOM = 33 + 125}$ So ${m\angle LOM = 158}$.